Effective radiated power

Effective radiated power (ERP), synonymous with equivalent radiated power, is an IEEE standardized definition of directional radio frequency (RF) power transmitted from a theoretical half-wave dipole antenna. It is differentiated from effective (or equivalent) isotropic radiated power (EIRP) mainly by use of relative antenna gain instead of absolute gain in the calculation. In the case of ERP, antenna gain is calculated as compared to the maximum directivity of a half-wave dipole antenna, whereas EIRP is calculated using antenna gain referenced to an ideal isotropic radiator, otherwise known as "absolute" gain. The term "antenna gain" is assumed to be absolute (referenced to isotropic) unless specifically stated to be relative. The gain is then multiplied by the power actually accepted by the antenna to result in the actual ERP value (or EIRP). Power losses which occur prior to the antenna, e.g., in the transmission line or from inefficiency in the generator itself are therefore not included in the calculation of ERP or EIRP.

Antenna gain is closely related to directivity and often incorrectly used interchangeably. However, gain is always less than directivity by a factor called radiation efficiency, η. Whereas directivity is entirely a function of wavelength and the geometry and type of antenna, gain takes into account the losses that always occur in the real world. Specifically, accelerating charge (time varying current) causes electromagnetic radiation per Maxwell's equations. Therefore, antennas use a current distribution on radiating elements to generate electromagnetic energy that propagates away from the antenna. This coupling is never 100% efficient (by Laws of Thermodynamics), and therefore antenna gain will always be less than directivity by this efficiency factor.

Because ERP is calculated as antenna gain (in a given direction) as compared to the maximum directivity of a half-wave dipole antenna, it creates a mathematically virtual effective dipole antenna oriented in the direction of the receiver. In other words, a notional receiver in a given direction from the transmitter would receive the same power if the source were replaced with an ideal dipole oriented with maximum directivity and matched polarization towards the receiver and with an antenna input power equal to the ERP. The receiver would not be able to determine a difference. Maximum directivity of an ideal half-wave dipole is a constant, i.e., 0 dBd = 2.15 dBi. Therefore, ERP is always 2.15 dB less than EIRP. The ideal dipole antenna could be further replaced by an isotropic radiator (a purely mathematical device which cannot exist in the real world), and the receiver cannot know the difference so long as the input power is increased by 2.15 dB.

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